Given:
A line through the points (7,1,-5) and (3,4,-2).
To find:
The parametric equations of the line.
Solution:
Direction vector for the points (7,1,-5) and (3,4,-2) is
Now, the perimetric equations for initial point with direction vector
, are
The initial point is (7,1,-5) and direction vector is . So the perimetric equations are
Similarly,
Therefore, the required perimetric equations are and
.
Any rhombus is a parallelogram, but not the other way around. If you were to make a Venn Diagram, the "rhombus" portion is entirely inside the set of "parallelograms".
The same can be said about rectangles as well. Any rectangle is a parallelogram, but not the other way around.
If we overlapped the region of rectangles and rhombuses, then we form the region for squares. A square is a combination of a rhombus and a rectangle.
Any square has all four sides the same length (property of a rhombus) and all angles equal to 90 (property of a rectangle). Since a square inherits properties of a rectangle and rhombus, it automatically makes any square a parallelogram.
Check out the venn diagram below.
